During the 10th Seminar on Analysis of Algorithms, MSRI, Berkeley, June 2004, Knuth posed the problem of analyzing the left and the right path length in a random binary trees. In particular, Knuth asked about properties of the generating function of the joint distribution of the left and the right path lengths. In this paper, we mostly focus on the asymptotic properties of the distribution of t...

The Painlevé test is very useful to construct not only the Laurent-series solutions but also the elliptic and trigonometric ones. Such single-valued functions are solutions of some polynomial first order differential equations. To find the elliptic solutions we transform an initial nonlinear differential equation in a nonlinear algebraic system in parameters of the Laurent-series solutions of t...

The Hénon–Heiles system in the general form has been considered. In two nonintegrable cases with the help of the Painlevé test new special solutions have been found as Laurent series, depending on three parameters. The obtained series converge in some ring. One of parameters determines a location of the singularity point, other parameters determine coefficients of series. For some values of the...

solitary wave solutions to the broer-kaup equations and approximate long water wave equa-tions are considered challenging by using the rst integral method.the exact solutions obtainedduring the present investigation are new. this method can be applied to nonintegrable equa-tions as well as to integrable ones.

in this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. we use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. finally, one example is given to illustrate our results.

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

For each Painlevé system, we have a manifold, called the defining manifold, on which the system defines a uniform foliation. In this paper, we describe confluence processes in these manifolds as deformations of manifolds compatible to those in Painlevé systems.

abstract disc infiltrometer is one of those devices that used in recent years in measurement of hydraulic conductivity of entire soil. in order to analyze the data taken by disc infiltrometer a variety of methods based on wooding’s base analyze have been introduced. the objective of this study was to compare the performances of ankeny and weir methods for predicting soil hydraulic properties us...